"might as well" versus "would rather / sooner"

-Is "might as well" used for the choice of the lesser of two evils whereas "would rather / sooner" for choice among good things?-Is "might as well" for something in the past while "may as well" for the non-past? So the sentence 1 below refers to existing marriage, doesn't it? For coming marriage, I should say "may as well" instead, shouldn't I? Sometimes I wonder if the usage is consistent with "might" and "may" as well as "could" and "can" where the past tense is used simply in less assertive mode as I have understood. -Is "might/may as well... as..." like examples below grammatical and common in usage? -Are "would rather" and "would sooner" like sentence 7 and sentence 8 below identical in usage and interchangeable? 1. I might as well marry a bird as marry you.2. You may as well start at once as stay here.3. I might as well die as marry such a man.4. We might as well walk home as try to catch a taxi here.5. I may as well throw the money away as give it to him.6. We might as well eat dog food as eat such a dish.7. I would rather stay at home than go out in this hot weather.8. I would sooner die than give up.